We have investigated the glass transitions of trihydric alcohols using broadband dielectric spectroscopy, and compare the results with those previously reported for sugar alcohols. Although a systematic glass transition feature related to molecular size has been reported for sugar alcohols, the essential factor governing this feature is still unclear because the number of carbon atoms (N C ) and the number of OH groups (N OH ) per molecule are identical in sugar alcohols. By examining trihydric alcohols (N C = N OH ), we conclude that N OH is dominant for the characteristics of the slow dynamics, such as fragility and glass transition temperature. This result suggests that the topological structure of the hydrogen-bonding network (coordination number) plays an important role in the glass transition of polyhydric alcohols. Furthermore, the orientational correlation factor evaluated using the Kirkwood-Fröhlich theory reveals a similarity in hydrogen bond formation among a variety of polyhydric alcohols. Based on these two experimental results, we discuss a possible physical picture of the glass transition of polyhydric alcohols.